Eric Tressler etressle@math.ucsd.edu Graduate Student Department of Mathematics University of California, San Diego My advisor is Ronald Graham. My research is mostly in the area of Ramsey theory, particularly Ramsey theory on the integers and Euclidean Ramsey theory. I also have broad interests in combinatorics in general, including graph structure theory, extremal set theory, and additive combinatorics. I also enjoy recreational mathematics: at UCSD, I've given talks about Conway's Angel problem and hat-guessing games.

Here you can find my vita, research statement, and teaching statement.

Java Applets
Fractal tree	Apollonian gaskets	Double pendulum Two double pendula	Fish swarm
These Java applets are intended as toys to put some interesting mathematical structures on display in a simple, interactive way. If you're interested in the mathematics behind anything here (or if you have comments), email me and I will be happy to talk about the details.

Papers
Monochromatic Triangles in $\E^2$	This paper is a survey of the current state of some Euclidean Ramsey problems arising from the work of Erdős, Graham, Montgomery, Rothschild, Spencer, and Straus. It includes a few new results. To appear in Geombinatorics.
The First Nontrivial Hales-Jewett Number is Four	Written with Neil Hindman. We prove that the Hales-Jewett number HJ(3,2) is 4; that is, if the length 4 words over the alphabet {1,2,3} are 2-colored, there must exist a monochromatic combinatorial line. Some lower bounds are also stated; the proofs of these are not included in the paper, but they can be found here. Accepted to Ars Combinatoria.
Open Problems in Euclidean Ramsey Theory	Written with Ron Graham. We examine some open problems in Euclidean Ramsey theory, focusing on those areas most active in recent years. Submitted.
Intersecting Domino Tilings	Written with Steve Butler and Paul Horn. We consider a variant of the Erdős-Ko-Rado problem in which our objects are tilings of regions by dominos. We say that two tilings intersect if they each have some domino in common. We completely characterize a maximal intersecting set for tilings of 2 × n and 3 × 2n strips. Submitted.